Free AMCAT Logical Reasoning: Syllogisms Questions and Answers 1 — Questions and Answers
Question 1: Statements: 1. All cats are animals. 2. All tigers are cats. Conclusions: I. All tigers are animals. II. All animals are tigers.
- Only conclusion I follows (Correct answer)
- Only conclusion II follows
- Both I and II follow
- Neither I nor II follows
Correct answer: Only conclusion I follows
From statement 2, 'tigers' is a subset of 'cats'. From statement 1, 'cats' is a subset of 'animals'. Therefore, 'tigers' must be a subset of 'animals', making conclusion I valid. Conclusion II is a reversal and is not necessarily true; there can be animals that are not tigers.
Question 2: Statements: 1. Some actors are singers. 2. All singers are dancers. Conclusions: I. Some actors are dancers. II. No singer is an actor.
- Only conclusion I follows (Correct answer)
- Only conclusion II follows
- Either I or II follows
- Neither I nor II follows
Correct answer: Only conclusion I follows
Since all singers are dancers, the group of actors who are singers must also be dancers. This makes conclusion I valid. Conclusion II directly contradicts the first statement ('Some actors are singers'), so it is invalid.
Question 3: Statements: 1. All pens are pencils. 2. No pencil is a marker. Conclusions: I. No pen is a marker. II. Some markers are pens.
- Both I and II follow
- Only conclusion II follows
- Only conclusion I follows (Correct answer)
- Neither I nor II follows
Correct answer: Only conclusion I follows
If all pens are inside the 'pencil' category, and the 'pencil' category has no overlap with the 'marker' category, then it logically follows that the 'pen' category can have no overlap with the 'marker' category. Conclusion I is valid, and Conclusion II is impossible.
Question 4: Statements: 1. Some papers are files. 2. Some files are books. Conclusions: I. Some papers are books. II. Some books are papers.
- Only conclusion I follows
- Only conclusion II follows
- Both I and II follow
- Neither I nor II follows (Correct answer)
Correct answer: Neither I nor II follows
There is an overlap between 'papers' and 'files', and an overlap between 'files' and 'books'. However, there is no definite information about the relationship between 'papers' and 'books'. The part of 'files' that overlaps with 'papers' might be completely different from the part that overlaps with 'books'. Therefore, neither conclusion is definite.
Question 5: Statements: 1. All buildings are houses. 2. No house is an apartment. Conclusions: I. No building is an apartment. II. All apartments are buildings.
- Only conclusion I follows (Correct answer)
- Only conclusion II follows
- Both I and II follow
- Neither I nor II follows
Correct answer: Only conclusion I follows
Since the entire category of 'buildings' is within the 'houses' category, and the 'houses' category is completely separate from the 'apartments' category, it must be true that 'buildings' and 'apartments' are also completely separate. Thus, conclusion I is correct. Conclusion II is impossible based on the statements.
Question 6: Statements: 1. Some dogs are cats. 2. Some cats are rats. Conclusions: I. Some dogs are rats. II. No dog is a rat.
- Only conclusion I follows
- Only conclusion II follows
- Either I or II follows
- Neither I nor II follows (Correct answer)
Correct answer: Neither I nor II follows
Because both statements are particular ('Some'), there is no definite relationship established between 'dogs' and 'rats'. The cats that are dogs could be different from the cats that are rats. However, the conclusions I and II form a complementary pair. One of them must be possible, but neither is certain, so we cannot definitively say either follows.
Question 7: Statements: 1. No fruit is a vegetable. 2. All potatoes are vegetables. Conclusions: I. No potato is a fruit. II. Some potatoes are fruits.
- Only conclusion I follows (Correct answer)
- Only conclusion II follows
- Both I and II follow
- Neither I nor II follows
Correct answer: Only conclusion I follows
The statements establish that the categories 'fruit' and 'vegetable' are mutually exclusive. Since 'potatoes' are entirely within the 'vegetable' category, they cannot have any overlap with the 'fruit' category. Therefore, conclusion I is valid, and conclusion II is invalid.
Free AMCAT Logical Reasoning: Syllogisms Questions and Answers 1
Statements:
1.
All cats are animals.
2.
All tigers are cats.
Conclusions:
I.
All tigers are animals.
II.
All animals are tigers.